• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.519-525
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• 2008

Let f be a diffeomorphisms of a compact $C^{\infty}$ manifold, and let p be a hyperbolic periodic point of f. In this paper, we prove that if generically, f is tame diffeomorphims then the following conditions are equivalent: (i) f is ${\Omega}$-stable, (ii) f has the $C^1$-stable shadowing property (iii) f has the $C^1$-stable inverse shadowing property.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.673-688
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• 2011

Let $n{\geq}2$ be an even integer. We investigate that if an odd mapping f : X ${\rightarrow}$ Y satisfies the following equation $2_{n-2}C_{\frac{n}{2}-1}rf\(\sum\limits^n_{j=1}{\frac{x_j}{r}}\)\;+\;{\sum\limits_{i_k{\in}\{0,1\} \atop {{\sum}^n_{k=1}\;i_k={\frac{n}{2}}}}\;rf\(\sum\limits^n_{i=1}(-1)^{i_k}{\frac{x_i}{r}}\)=2_{n-2}C_{{\frac{n}{2}}-1}\sum\limits^n_{i=1}f(x_i),$ then f : X ${\rightarrow}$ Y is additive, where $r{\in}R$. We also prove the stability in normed group by using shadowing property and the Hyers-Ulam stability of the functional equation in Banach spaces and in Banach modules over unital C-algebras. As an application, we show that every almost linear bijection h : A ${\rightarrow}$ B of unital $C^*$-algebras A and B is a $C^*$-algebra isomorphism when $h(\frac{2^s}{r^s}uy)=h(\frac{2^s}{r^s}u)h(y)$ for all unitaries u ${\in}$ A, all y ${\in}$ A, and s = 0, 1, 2,....

• Communications of the Korean Mathematical Society
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• v.16 no.1
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• pp.119-124
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• 2001

In the paper we show that some operators defined on L$^1$($\mu$) and on C(K) into Banach space with the RNP have the lifting property.

• Journal of the Korean Wood Science and Technology
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• v.38 no.2
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• pp.101-107
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• 2010

Heat treatment was performed to improve sound absorption properties for four tree species; Tulip tree, Korean Paulownia, Red pine and Costata birch, at temperature of $175^{\circ}C$ and $200^{\circ}C$under vacuum condition. Sound absorption properties of two kinds of boards, which were in radial and tangential sections, were measured under a frequency range of 100 to 3200 Hz by the two microphone transfer function method. It was found that sound absorption properties were increased by heat treatment and the efficiency was higher at $200^{\circ}C$ than that at $175^{\circ}C$. Even Costata birch had a little effect on low temperature of $175^{\circ}C$, $200^{\circ}C$ heat treatment for sound absorption property, the efficiencies of sound absorption were 14, 19%, respectively. The efficiencies of sound absorption ranged 22 to 120% for heat-treated Tulip tree, Korean Paulownia.

• Journal of Korea Foundry Society
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• v.20 no.4
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• pp.254-259
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• 2000

Metal matrix composites(MMCs) reinforced with hard particles have many potential application in aerospace structures, auto parts, semiconductor package, heat resistant panels, wear resistant materials and so on. In this work, the effect of SiC partioel sizes(50 and 100 ${\mu}m$) and additional elements such as Si, Cu and Ti on the microstructure and the wear property of $Al-5Mg-X(Si,Cu,Ti)/SiC_p$ composites produced by pressureless infiltration method have been investigated using optical microscopy, scanning eletron microcopy(SEM) with EDS(energy dispersive spectrometry), hardness test, X-ray diffractometer(XRD) and wear test. In present study, the sound $Al-5Mg-X(Si,Cu,Ti)/SiC_p$(50 and 100 ${\mu}m$) composites were fabricated by pressureless infiltration method. The $Al-5Mg-0.3Si-O.1Cu-O.1Ti/SiC_p$ composite with $50 {\mu}m$ size of SiC particle has higher hardness and better wear property than any other composite with $100{\mu}m$ size of SiC particle produced by pressureless infiltration method. The hardness and wear property of $Al-5Mg/SiC_p$(50 and 100 ${\mu}m$) composites were enhanced by the addition of Si, Cu and Ti in Al-5%Mg matrix alloy.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.167-175
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• 2018

In this paper we show that two notions of the average shadowing property and the hyperbolicity are equivalent in linear dynamical systems on the vector space ${\mathbb{C}}^n$.

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.765-780
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• 2015

We consider the problem of characterizing the palindromic sequences ${\langle}c_{d-1},\;c_{d-2}\;,{\cdots},\;c_0\rangle$, $c_{d-1}{\neq}0$, having the property that for any $K{\in}\mathbb{N}$ there exists a number that is a palindrome simultaneously in K different bases, with ${\langle}c_{d-1},\;c_{d-2}\;,{\cdots},\;c_0\rangle$ being its digit sequence in one of those bases. Since each number is trivially a palindrome in all bases greater than itself, we impose the restriction that only palindromes with at least two digits are taken into account. We further consider a related problem, where we count only palindromes with a fixed number of digits (that is, d). The first problem turns out not to be very hard; we show that all the palindromic sequences have the required property, even with the additional point that we can actually restrict the counted palindromes to have at least d digits. The second one is quite tougher; we show that all the palindromic sequences of length d = 3 have the required property (and the same holds for d = 2, based on some earlier results), while for larger values of d we present some arguments showing that this tendency is quite likely to change.

• The Korean Journal of Food And Nutrition
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• v.27 no.1
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• pp.112-119
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• 2014

Ohmic heating uses electric resistance heat which occurs equally and rapidly inside food when the electrical current is transmitted into. Prior to the study, we have researched the potato starch's thermal property changes during ohmic heating. Comparing with conventional heating, the gelatinization temperature and the range of potato starch treated by ohmic heating are increased and narrowed respectively. Herein, we have studied thermal property changes of wheat, corn, potato and sweet potato starch by ohmic heating as well as conventional heating. And then we measure the water holding capacity of starches. Annealing of starch is a heat treatment method heated at 3~4% below the gelatinization point. This treatment changes the starch's thermal property. In the DSC analysis of this study, the $T_o$, $T_p$, $T_c$ of all starch levels have increased, and the $T_c$-$T_o$ narrowed. In the ohmic heating, the treatment sample is extensively changed but not with the conventional heating. From the ohmic treatment, increases from gelatinization temperature are potato ($8.3^{\circ}C$) > wheat ($5.3^{\circ}C$) > corn ($4.9^{\circ}C$) > sweet potato ($4.5^{\circ}C$), and gelatinization ranges are potato ($7.9^{\circ}C$), wheat ($7.5^{\circ}C$), corn ($6.1^{\circ}C$) and sweet potato ($6.8^{\circ}C$). In the case of conventional treatment, water holding capacity is not changed with increasing temperature but the ohmic heating is increased. Water holding capacity is related to the degree of gelatinization for starch. This result show that when treated with below gelatinization temperature, the starches are partly gelatined by ohmic treatment. When viewing the results of the above, ohmic treatment is enhanced by heating and generating electric currents to the starch structure.

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.101-110
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• 2005

Let (X, D; ${\Gamma}$) be a G-convex space and Y a Hausdorff space. Then $U^K_C$(X, Y) ${\subset}$ KD(X, Y), where $U^K_C$ is an admissible class (dup to Park) and KD denotes the class of multimaps having the KKM property for open-valued multimaps. This new result is used to obtain a KKM type theorem, matching theorems, a fixed point theorem, and a coincidence theorem.

• International Journal of Industrial Entomology and Biomaterials
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• v.37 no.1
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• pp.29-32
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• 2018

Silkworm powder's thermal property is an important factor for its storage and marketing. This study examined the effect of edible enzyme on the thermal property of silkworm powder using Thermogravimetric Analysis (TGA) and Differential Scanning Calorimetry (DSC). Results of the TGA showed that regardless of the enzyme treatment, the weight loss patterns of silkworm powders exhibited 3 step thermal property deterioration at approximately $80^{\circ}C$, $280^{\circ}C$, and $480^{\circ}C$ due to water evaporation and thermal degradation. This is similar with the DSC which also resulted in all samples two endothermic peaks attributed also to water evaporation and thermal degradation. These results indicated that the use of enzyme such as protease and cellulase might not affect significantly the thermal properties of silkworm powder.